Are polymer melts "ideal"?

It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display random-walk conformational properties without long-range correlations between subsequent bonds. This absence of memory means, for instance, that the bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain should exponentially decay with $s$. Presenting numerical results and theoretical arguments for both monodisperse chains and self-assembled (essentially Flory size-distributed) equilibrium polymers we demonstrate that some long-range correlations remain due to self-interactions of the chains caused by the chain connectivity and the incompressibility of the melt. Suggesting a profound analogy with the well-known long-range velocity correlations in liquids we find, for instance, $P(s)$ to decay algebraically as $s^{-3/2}$. Our study suggests a precise method for obtaining the statistical segment length \bstar in a computer experiment.Comment: 4 pages, 3 figure

Mode-coupling theory for structural and conformational dynamics of polymer melts

A mode-coupling theory for dense polymeric systems is developed which unifyingly incorporates the segmental cage effect relevant for structural slowing down and polymer chain conformational degrees of freedom. An ideal glass transition of polymer melts is predicted which becomes molecular-weight independent for large molecules. The theory provides a microscopic justification for the use of the Rouse theory in polymer melts, and the results for Rouse-mode correlators and mean-squared displacements are in good agreement with computer simulation results.Comment: 4 pages, 3 figures, Phys. Rev. Lett. in pres

Static and dynamic properties of large polymer melts in equilibrium

We present a detailed study of the static and dynamic behavior of long semiflexible polymer chains in a melt. Starting from previously obtained fully equilibrated high molecular weight polymer melts [{\it Zhang et al.} ACS Macro Lett. 3, 198 (2014)] we investigate their static and dynamic scaling behavior as predicted by theory. We find that for semiflexible chains in a melt, results of the mean square internal distance, the probability distributions of the end-to-end distance, and the chain structure factor are well described by theoretical predictions for ideal chains. We examine the motion of monomers and chains by molecular dynamics simulations using the ESPResSo++ package. The scaling predictions of the mean squared displacement of inner monomers, center of mass, and relations between them based on the Rouse and the reptation theory are verified, and related characteristic relaxation times are determined. Finally we give evidence that the entanglement length $N_{e,PPA}$ as determined by a primitive path analysis (PPA) predicts a plateau modulus, $G_N^0=\frac{4}{5}(\rho k_BT/N_e)$, consistent with stresses obtained from the Green-Kubo relation. These comprehensively characterized equilibrium structures, which offer a good compromise between flexibility, small $N_e$, computational efficiency, and small deviations from ideality provide ideal starting states for future non-equilibrium studies.Comment: 13 pages, 10 figures, to be published in J. Chem. Phys. (2016

Lattice Monte Carlo Simulations of Polymer Melts

We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction $0.5$. In order to reduce the local density fluctuations, we test a pre-packing process for the preparation of the initial configurations of the polymer melts, before the excluded volume interaction is switched on completely. This process leads to a significantly faster decrease of the number of overlapping monomers on the lattice. This is useful for simulating very large systems, where the statistical properties of the model with a marginally incomplete elimination of excluded volume violations are the same as those of the model with strictly excluded volume. We find that the internal mean square end-to-end distance for moderately stiff chains in a melt can be very well described by a freely rotating chain model with a precise estimate of the bond-bond orientational correlation between two successive bond vectors in equilibrium. The plot of the probability distributions of the reduced end-to-end distance of chains of different stiffness also shows that the data collapse is excellent and described very well by the Gaussian distribution for ideal chains. However, while our results confirm the systematic deviations between Gaussian statistics for the chain structure factor $S_c(q)$ [minimum in the Kratky-plot] found by Wittmer et al.~\{EPL {\bf 77} 56003 (2007).\} for fully flexible chains in a melt, we show that for the available chain length these deviations are no longer visible, when the chain stiffness is included. The mean square bond length and the compressibility estimated from collective structure factors depend slightly on the stiffness of the chains.Comment: 15 pages, 12 figure

Soft and Hard Implant Fabrication Using 3D-Bioplotting TM

At the Freiburger Materialforschungszentrum we have developed a new process (3DBioplotting TM) that permits most kind of polymers and biopolymers to be used in 3D scaffold design, including hydrogels (e.g. collagen, agar), polymer melts (e.g. PLLA, PGA, PCl) and twocomponent systems (e.g. chitosan, fibrin). Cells can be incorporated within the construction process, making this an ideal Rapid Prototyping technique for Organ Printing. Tailor-made biodegradable soft or hard scaffolds can so be fabricated in a short time using individual computer-tomography data from the patient. In-vitro tests showed promising results and in-vivo experiments are now under observation.Mechanical Engineerin

Dynamics of polymers: classic results and recent developments

In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers reference, we start with a short review of the equilibrium static properties of polymer systems. Most attention is paid to the dynamics of unentangled polymer systems, where apart from classical Rouse and Zimm models we review some recent scaling and analytical generalizations. The dynamics of systems with entanglements is also briefly reviewed. Special attention is paid to the discussion of comparatively weakly understood topological states of polymer systems and possible approaches to the description of their dynamics

Equilibration of High Molecular-Weight Polymer Melts: A Hierarchical Strategy

A strategy is developed for generating equilibrated high molecular-weight polymer melts described with microscopic detail by sequentially backmapping coarse-grained (CG) configurations. The microscopic test model is generic but retains features like hard excluded volume interactions and realistic melt densities. The microscopic representation is mapped onto a model of soft spheres with fluctuating size, where each sphere represents a microscopic subchain with $N_{\rm b}$ monomers. By varying $N_{\rm b}$ a hierarchy of CG representations at different resolutions is obtained. Within this hierarchy, CG configurations equilibrated with Monte Carlo at low resolution are sequentially fine-grained into CG melts described with higher resolution. A Molecular Dynamics scheme is employed to slowly introduce the microscopic details into the latter. All backmapping steps involve only local polymer relaxation thus the computational efficiency of the scheme is independent of molecular weight, being just proportional to system size. To demonstrate the robustness of the approach, microscopic configurations containing up to $n=1000$ chains with polymerization degrees $N=2000$ are generated and equilibration is confirmed by monitoring key structural and conformational properties. The extension to much longer chains or branched polymers is straightforward

Static Rouse Modes and Related Quantities: Corrections to Chain Ideality in Polymer Melts

Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (`hard monomers') to no excluded volume (`phantom chains'). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.Comment: 9 pages, 7 figures, accepted for publication in EPJ